DETROIT — The NBA held internal discussions about the Knicks’ decision to keep J.R. Smith’s brother, Chris Smith, on their 15-man roster and ultimately decided it was not in violation of circumventing the salary cap, The Post has learned.

On Monday, the Knicks sent Smith to their D-League affiliate in Erie, Pa. as planned, but he still is part of the 15-man roster. It has caused consternation with the fan base because the Knicks have five point guards on the roster, but were lacking in healthy big men even before Tyson Chandler’s leg injury.

The NBA began discussing the issue internally after coach Mike Woodson said before the preseason cut deadline J.R.’s presence was a factor in whether the team kept Chris Smith.

J.R. Smith was a free agent over the summer and talked about taking less money to stay with the Knicks, who could offer only the early-Bird exception that, under the terms of the collective bargaining agreement, started at $5.5 million. When the undrafted Chris Smith changed agents to J.R.’s rep, Leon Rose, last spring, some in the league saw it as a “package deal.’’

But, according to a league official, the league decided Chris Smith was enough of a bona fide NBA prospect to justify the club keeping him.

“Chris has enough talent,’’ the official told The Post. “He could become an NBA player one day. Some teams do keep projects instead of players who can help right away, and Chris is one of those projects.”

Chris Smith, who played at Louisville, joined Erie’s training camp Monday after essentially being a practice player for the Knicks. He was inactive for eight games and dressed for one but didn’t play. During preseason, Chris Smith, coming off knee surgery, shot 1-of-7 from the field in 20 minutes.

While Chris Smith makes the league minimum $491,000, he is actually costing the Knicks $2.1 million when factoring in the Knicks’ luxury-tax bracket. Worse, his contract, because of a quirky addendum, became fully guaranteed on opening night.

Late last month, Woodson said J.R. Smith’s presence gave his brother a better chance of making the team.

“Sure, it does,” Woodson said at the time. “I look at [Chris] just like I look at J.R., though J.R. is the guy who played in a uniform and has been very productive for us. I have a great deal of respect for that family. That’s his brother. I respect that.’’

Smith’s inclusion on the Knicks roster led to a Twitter feud between J.R. Smith and guard Brandon Jennings of the Pistons, whom the Knicks face Tuesday in Detroit. Jennings tweeted he can’t believe Chris Smith had an NBA roster spot while his friends, Bobby Brown and Pooh Jeter, are playing in China.

J.R. Smith responded he’d send his “street homies’’ to Detroit and the NBA fined him $25,000. A league official told The Post the league viewed the tweet as “an implied threat.’’

Over the weekend, Jennings told Detroit reporters the initial tweet was meant to support his two friends, not denigrate Smith.

“Regardless if the tweet was accurate or not, sometimes maybe there are things I should discuss with the homies rather than let the world know about it,” Jennings said.